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Proofgold Proof

pf
Let x0 of type ιο be given.
Let x1 of type ιιιο be given.
Let x2 of type ιι be given.
Let x3 of type ιιιιιι be given.
Let x4 of type ιιιιι be given.
Let x5 of type ιιιιι be given.
Let x6 of type ιιιιιιι be given.
Assume H0: MetaCat_equalizer_struct_p x0 x1 x2 x3 x4 x5 x6.
Let x7 of type ι be given.
Let x8 of type ι be given.
Assume H1: x0 x7.
Assume H2: x0 x8.
Let x9 of type ι be given.
Let x10 of type ι be given.
Assume H3: x1 x8 x7 x9.
Assume H4: x1 x8 x7 x10.
Apply unknownprop_6fb40ae90c2353c48cea13941af2c687babb3dd98aeca853d92abaa494eed2c0 with x0, x1, x2, x3, x8, x7, x9, x10, x4 x8 x7 x9 x10, x5 x8 x7 x9 x10, x6 x8 x7 x9 x10.
Apply H0 with x8, x7, x9, x10 leaving 4 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
The subproof is completed by applying H4.